What causes hormonal contraception to not work?

Human error is the main culprit. Not taking it the same time every day, forgetting it, that kind of thing.

There are also special cases when it won't work. Specifically, when women approach menopause, they tend to have very high FSH (FSH is the hormone made by the pituitary that stimulates the ovary to make eggs). Taking birth control pills suppresses FSH so the ovary never gets a message to make eggs. Because FSH is so high in some women approaching menopause, the pills don't suppress it enough to prevent eggs from growing. So that's one type of instance when it doesn't work.